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Error syndromes for heavy hexagonal code and other topological codes such as surface code have typically been decoded by using Minimum Weight Perfect Matching (MWPM) based methods. Recent advances have shown that topological codes can be…
We propose a Bayesian tensor-on-tensor regression approach to predict a multidimensional array (tensor) of arbitrary dimensions from another tensor of arbitrary dimensions, building upon the Tucker decomposition of the regression…
Tensor train (TT) decomposition provides a space-efficient representation for higher-order tensors. Despite its advantage, we face two crucial limitations when we apply the TT decomposition to machine learning problems: the lack of…
Matching is one of the simplest approaches for estimating causal effects from observational data. Matching techniques compare the observed outcomes across pairs of individuals with similar covariate values but different treatment statuses…
Tensor decomposition (TD) is widely used in hyperspectral image (HSI) compression. The initialization of factor matrix in tensor decomposition can determine the HSI compression performance. It is worth noting that HSI is highly correlated…
The tailored coupled cluster (TCC) approach is a promising ansatz that preserves the simplicity of single-reference coupled cluster theory, while incorporating a multi-reference wave function through amplitudes obtained from a preceding…
Tensor train decomposition is widely used in machine learning and quantum physics due to its concise representation of high-dimensional tensors, overcoming the curse of dimensionality. Cross approximation-originally developed for…
Quantum-mechanical methods are widely used for understanding molecular interactions throughout biology, chemistry, and materials science. Quantum diffusion Monte Carlo (DMC) and coupled cluster with single, double, and perturbative triple…
We develop and test methods that include second and third-order perturbation theory (MP3) using orbitals obtained from regularized orbital-optimized second-order perturbation theory, $\kappa$-OOMP2, denoted as MP3:$\kappa$-OOMP2. Testing…
In quantum chemistry, one of the most important challenges is the static correlation problem when solving the electronic Schr\"odinger equation for molecules in the Born--Oppenheimer approximation. In this article, we analyze the tailored…
Modeling inverse dynamics is crucial for accurate feedforward robot control. The model computes the necessary joint torques, to perform a desired movement. The highly non-linear inverse function of the dynamical system can be approximated…
Interpretation of electrocardiography (ECG) signals is required for diagnosing cardiac arrhythmia. Recently, machine learning techniques have been applied for automated computer-aided diagnosis. Machine learning tasks can be divided into…
This paper introduces a tensor neural network (TNN) to address nonparametric regression problems, leveraging its distinct sub-network structure to effectively facilitate variable separation and enhance the approximation of complex,…
Tensor hypercontraction is a method that allows the representation of a high-rank tensor as a product of lower-rank tensors. In this paper, we show how tensor hypercontraction can be applied to both the electron repulsion integral (ERI)…
The investment on the stock market is prone to be affected by the Internet. For the purpose of improving the prediction accuracy, we propose a multi-task stock prediction model that not only considers the stock correlations but also…
A rising problem in the compression of Deep Neural Networks is how to reduce the number of parameters in convolutional kernels and the complexity of these layers by low-rank tensor approximation. Canonical polyadic tensor decomposition…
Most state of the art deep neural networks are overparameterized and exhibit a high computational cost. A straightforward approach to this problem is to replace convolutional kernels with its low-rank tensor approximations, whereas the…
Cross-correlation techniques provide a promising avenue for calibrating photometric redshifts and determining redshift distributions using spectroscopy which is systematically incomplete (e.g., current deep spectroscopic surveys fail to…
This paper proposes a novel method for learning highly nonlinear, multivariate functions from examples. Our method takes advantage of the property that continuous functions can be approximated by polynomials, which in turn are representable…
Hyperdimensional computing (HDC) offers lightweight learning for energy-constrained devices by encoding data into high-dimensional vectors. However, its reliance on ultra-high dimensionality and static, randomly initialized hypervectors…